РЕШЕНИЯ ЗАДАНИЯ ДЛЯ ВЫПУСКНОГО ЭКЗАМЕНА ПО АЛГЕБРЕ И НАЧАЛАМ АНАЛИЗА 11-класс 6-задание

6-njy iş. Çep tarap
1.Aňlatmany ýönekeýleşdiriň:
a-ba34+a12b14-a12-b12a14+b14∙aa14b12-b34 = a-b-a+a12-b12a12(a14+b14) · ab12(a14-b14) =
= a(a12b12-b )a12b12(a12-b12) = ab12(a12-b12 )a12b12(a12-b12) = aa12 = a12 = a ;
Jogaby: a ;
2. Deňlemäni çözüň:
4-lgx=3lgx; lgx+3lgx-4=0; (lgx+4)(lgx-1)=0;
lgx-4=0; lgx≠4; lgx-1=0; lgx=1; lgx=1; x=10;
Jogaby: x=10;
3.Deňsizligi çözüň:
x2+2x-3x+1≥0; (x+3)(x-1)x+1≥0; x≠ -1;
(-∞; 3) э -4; (-4+3)(-4-1)-4+1 = (-1)(-5-3 <0;
(-3; 3) э -2; (-2+3)(-2-1)-2+1 = 1·(-3-1 >0;
(-1; 1) э 0; (0+3)(0-1)0+1 = 3·(-11 = -31 <0;
(1; ∞) э 0; (2+3)(2-1)2+1 = 5·13 = 53 >0; x€[-3; -1]∪[1; +∞];
Jogaby: x€[-3; -1]∪[1; +∞];
4. -10,2; -9,5;… arifmetik progressiýanyň birinji položitel agzasyny tapyň.
a1= -10.2; a2= -9.5; an>0; an-? ; d= -9.5+10.2=0.7;
an= a1+(n-1)d= -10.2+(n-1)·0.7>0; n-1>10.20.7=14.5; n>15.5; n≈16;
an= a1+(n-1)d= -10.2+15·0.7 =-10.2+10.5= 0.3; Jogaby: 0.3;
5. Toždestwony subut ediň:
1-cos α+sinα1+cosα+sinα=tg α2; 1-cos α+sinα1+cosα+sinα = cos2⍺2 +sin2⍺2 -cos2⍺2+sin2⍺2+2sin⍺2cos ⍺2cos2⍺2 +sin2⍺2+cos2⍺2-sin2⍺2+2sin⍺2cos ⍺2 =
= 2sin⍺2(sin⍺2 +cos ⍺2 )2cos ⍺2 (sin⍺2+cos ⍺2 = sin⍺2cos ⍺2 = tg α2; Subut edildi.
6. fx=x-4x+5 funksiýanyň [1; 9] kesimde iň kiçi we iň uly bahalaryny tapyň.
f(x)= x-4x+5; [1,9]; fˊ(x)=1- 2x ; 1 = 2x ; x = 4;
x 1 (1;4) 4 (4;9) 9
fˊ(x -1 - 0 + 13f(x) 2 565554154800 1 1155704127500 2
min[1;9]fx= f(4)= 1; max[1;9]fx= f(1)=f(9)=2;
Jogaby: min[1;9]fx= f(4)= 1; max[1;9]fx= f(1)=f(9)=2;
7. Beýikligi 20 m bolan jaýyň üçeginden wertikal ýokarlygyna daş zyňlypdyr. Eger zyňlandan 1 sekuntdan soň daş bölegi ýerden 30 m ýokarda bolan bolsa, onda onuň başlangyç tizligi näçä deň?
73035117748Berlen:
H0= 20m,
t = 1 sekunt;
h=30m,
Tapmaly:
V0= x m/s
0Berlen:
H0= 20m,
t = 1 sekunt;
h=30m,
Tapmaly:
V0= x m/s
Çözülüşi:
h= h0 + V0·t - gt22 = 20m+xm - 9.82m;
xm= (10+4.9)m; x= 14.9;
Jogaby: V0= 14.9 m/s ;6-njy iş. Sag tarap
1. Aňlatmany ýönekeýleşdiriň:
a-ba14b12+b34-a12-b12a14+b14∙ba34-a12b34= a-b-a12b12+bb12a14 +b14∙ba12a14 -b14= = a12a12 -b12ba12b12a12 -b12 = bb12 = b12 = b ; Jogaby: b ; 2.Deňlemäni çözüň:
5-2lgx=3lgx; 2lgx+3lgx -5 =0; 2(lgx-1)( lgx +52) ;
lgx-1=0; x=10; lgx+ 52 ≠ 0; lgx≠ - 52; Jogaby: x=10;
3.Deňsizligi çözüň:
x2-x-2x-1≥0; (x-2)(x+1)x-1≥0; x ≠ 1; (- ∞; - 1) Э -2;
(-2-2)·(-2+1)-2-1 = (-4)·(-1)-3 = 4-3 <0; (-1; 1) Э 0; (-2)·1-1 >0;
(1; 2) Э 32 ; (-0,5)·0,250,5 < 0; (2; +∞) Э 3; 1·43-1 >0 ; =>x€ (-1; 1)∪ (2; +∞);
Jogaby: x€ (-1; 1)∪ (2; +∞);
4. 12,5; 11,2;… arifmetik progressiýanyň birinji otrisatel agzasyny tapyň.
a1=12.5, a2= 11.2, d= a2 - a1= 11.2-12.5 = - 1.3; an<0;
an= a1+(n-1)·d = 12.5 - (n-1)·1.3<0; n-1> 12.51.3 = 9.61 ; n> 10.61; n ≈ 11;
a11= a1+10·d = 12.5 -10·1.3 = 12.5 – 13 = -0.5 ; Jogaby: a11= -0.5;
5. Toždestwony subut ediň:
sin 2α-sinα1-cosα+cos 2α=tg α. sin 2α-sinα1-cosα+cos 2α = 2sinαcos⍶-sinαcos2α+sin2α-cosα+cos2α-sin2α =
= sinα(2cos α-1)cosα(2cosα-1) = = sinαcosα = tg α Subut edildi.
6. fx=x-4x+2+8 funksiýanyň [-1; 7] kesimde iň kiçi we iň uly bahalaryny tapyň.
f(x)= x-4x+2+8; [-1; 7]; )= 1- 2x+2 ; fˊ(x)= 0; 1- 2x+2=0; x=2;x -1 (-1;2) 2 (2;7) 7
fˊ(x -1 - 0 + 13f(x) 3 565554154800 2 1155704127500 3
min[-1;7]fx= f(2); max[-1;7]fx= f(-1)=f(7)=3;
Jogaby: min[-1;7]fx= f(2); max[-1;7]fx= f(-1)=f(7)=3;
7. Jaýyň üçeginden ϑ0=15 m/s başlangyç tizlik bilen wertikal ýokarlygyna daş zyňlypdyr. Eger zyňlandan 2 sekuntdan soň daş bölegi ýerden 30 m ýokarlykda bolan bolsa, onda jaýyň beýikligi näçe?
128841519789500Berlen:
V0=15m/s, Çözülüşi:
t = 2 sekunt,
h = 30 m, h=h0 + V0·t - 9t22 ; => h=h0 + V0·t - 9t22 =
-889728808800
Tapmaly; =30m – 30m+ 9.8·2m =19.6m;
h0 = xm- ?
Jogaby: 19.6m;